

A258064


Number of hands of n points in Spanish dominoes.


0



3, 9, 29, 67, 147, 283, 526, 893, 1470, 2287, 3451, 4990, 7030, 9559, 12697, 16375, 20664, 25406, 30621, 36034, 41618, 47022, 52174, 56696, 60548, 63362, 65186, 65746, 65186, 63362, 60548, 56696, 52174, 47022, 41618, 36034, 30621, 25406, 20664, 16375, 12697, 9559, 7030, 4990, 3451, 2287, 1470, 893, 526, 283, 147, 67, 29, 9, 3
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OFFSET

15,1


COMMENTS

In Spanish dominoes (double sixes) each of the four players gets a hand of seven stones. a(n) represents the number of possible different hands of n points. The lowest possible number of points in a hand is 15: (00 / 01 / 11 / 02 / 12 / 03) and one of the following stones: (22 / 13 / 04) which is three different combinations.
The highest hand is 69 points (66 / 65 / 55 / 64 / 54 / 63) and any of: (44 / 53 / 62). The sequence is finite and symmetrical around the peak: a(42) = 65746.
The sum of a(15) through a(69) is C(28,7) = 1184040.


LINKS

Table of n, a(n) for n=15..69.
Wikipedia, Dominoes, Tiles and suits


FORMULA

a(42+n) = a(42n).


EXAMPLE

a(15)=3 since there are only 3 combinations of 7 stones that yield a hand of 15 points.


MATHEMATICA

Last /@ Tally[ Sort[ Total /@ Flatten /@ Subsets[ Flatten[ Table[{i, j}  1, {i, 7}, {j, i}], 1], {7}]]] (* Giovanni Resta, Jun 23 2015 *)


CROSSREFS

Sequence in context: A047137 A058145 A218915 * A161590 A192245 A242558
Adjacent sequences: A258061 A258062 A258063 * A258065 A258066 A258067


KEYWORD

full,fini,nonn


AUTHOR

Sergio Pimentel, May 18 2015


STATUS

approved



